Solve the problem. For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of $x ^ { 2 }$ in a two-tailed hypothesis test with n=104 and $\alpha = 0.10$ A) X²=85.903 and X²=122.735 B) X²=81.186 and X²=128.520 C) X²=80.300 and X²=127.406 D) X²=84.992 and X²=121.646

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For a two-tailed test with $\alpha = 0.10$, the critical z-values are approximately $\pm 1.645$. Using the approximation formula for $\chi^2$, we calculate the lower and upper critical values for $k = 104$. The calculations yield values closest to those in option C.

Solve the Problem χ2\chi ^ { 2 }χ2 Values Can Be Approximated as Follows

Solve the Problem $\chi ^ { 2 }$ Values Can Be Approximated as Follows